Five times the difference between a number(x) and two
5 (x - 2)
Is greater than the quotient(means division) of two times the number and three
> 2x / 3
Combine the two
5 (x - 2) > 2x / 3
Multiply the 5 to x - 2
5x - 10 > 2x / 3
Multiply both sides by 3
(5x - 10) * 3 > (2x / 3) * 3
15x - 30 > 2x
Transpose -30 and 2x
15x - 2x > 30
Subtract 15x and 2x
13x > 30
Divide both by 13 to determine the value of x
13x/13 > 30/13
Therefore
x > 30/13 or 2.3076923076923077
Since we are looking for an integer it can't be in decimal or fractional form
Therefore x might be 2 or 3
Lets check by substituting the value of x to the equation
5 (2 - 2) > 2(2) / 3
Subtract 2 and 2
5 * 0 > 4 / 3
Multiply
Therefore
0 > 4/3 (or 1.33333...) incorrect
Let's try the other one
5(3 - 2) > 2(3) / 3
Subtract and multiply
5 * 1 > 6 / 3
Multiply and divide
5 > 2 Correct
Therefore
3 is the smallest integer that will satisfy the inequality
I hope it helps
